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elasticity, Microeconomics

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-1-
ASSIGNMENT #1
The demand function for Product X is given by:
Qdx = 80- 2Px- 0.05P²x -0.2Py + 4Pz + 0.01I+ 2A
Where:
Px
Price of good X
$120.00
Py
Price of related good y
$100.00
Pz
Price of related good z
$40.00
I
Income
$7000.00
A
Advertising
$250.00
a. (i) Calculate the own Price elasticity of demand (PED) for Good X.
(ii) Discuss whether revenue can be increased by increasing the price of Good X?
(iii) Illustrate on a well labelled demand graph for Product X, the Total Revenue earned when Price is equal to $120.00
[8 marks]
b. (i) Determine the Cross-Price elasticity of demand (XED) between Good X and Good Y.
(ii) Using your answer for b. (i), explain the relationship between Good X and Good Y. (Substitute, Complement etc)
(iii) Determine the Cross-Price elasticity of demand (XED) between Good X and Good Z.
(iv) Using your answer for b. (iii), explain the relationship between Good X and Good Z. (Substitute, Complement etc)
(v) Based on the solutions for parts b. (i) to (iv) above, suggest one example of an actual agricultural product that fits the description for each of the following: Product X, Product Y and Product Z.
[13 marks]
c. Consider the following two situations:
? Situation 1: There is a fifteen percent (15%) increase in the price of Good Z (Pz).
? Situation 2: There is a sixty percent (60%) decrease in the price of Good Y (Py).
-2-
Both situations highlighted above, will affect the Total Revenue earned by Producers of Good X. Explain which situation is more beneficial, to the producers of Good X, from a Total Revenue earned perspective.
[5 marks]
d. (i) Calculate the Income elasticity of demand (YED) for Good X.
(ii) Explain whether Good X is a normal good or an inferior good.
[4 marks]
e. Assume that the own Price elasticity of demand (PED) for Good X is -2 and the Income elasticity of Demand (YED) for Good X is 3.
(i) Calculate the percentage change in consumption that will occur, when income declines by twenty percent (20%) .
(ii) Using the demand function presented for Good X above, determine the new quantity of Good X demanded when income declines by twenty percent (20%) , and the Income Elasticity of Demand (YED) for Good X is 3.
[5 marks]
f. Suppose that the Cross-price elasticity of demand (XED) between Good X and Good Z is 4.
(i) How much would the price of Good Z (Pz) have to change in order to increase the consumption of Good X by twenty five percent (25%)?
(ii) Use a well-labelled illustration of the demand curve for Good X to show the effect on the demand for Good X, of the change in the Price of Good Z (PZ) as calculated in f. (i) above.

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